Finite Group Databasebeta

← C2×#13072823 #14922216

Subgroups — C2×#13072823 #14922216

Order 2816.

3070 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66949C211yesmaximal, characteristic, complemented
2C22×#66930C211yesmaximal, characteristic, complemented
3#13072823C2116yesmaximal, direct product factor
4C2×#10622271C211yesmaximal, characteristic, complemented
5C2×#10622288C211yesmaximal, characteristic, complemented
6C2×#10622572C211yesmaximal, characteristic
7C2×#10622560C211yesmaximal, characteristic, complemented
8C2×#10622259C211yesmaximal, characteristic, complemented
9C2×#10622282C211yesmaximal, characteristic, complemented
10C2×#10622546C211yesmaximal, characteristic, complemented
11C2×#10622591C211yesmaximal, characteristic, complemented
12C2×#10622571C211yesmaximal, characteristic
13C2×#10622569C211yesmaximal, characteristic
14C2×#10622559C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
16C2×C11×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D11C2211yescharacteristic
18C24×Dic11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C23×Dic22C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C42×C11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38C22×C4×Dic11C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40C2×#66949—28no—
41C2×#66949C2218yescomplemented
42C2×#66930—28no—
43C2×#66930C2218yescomplemented
44C11×#388C2218yescomplemented
45C2×C11×#95C2211yescharacteristic
46C2×C11×#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57#10622591C2218yescomplemented
58#10622572C2218yes—
59#10622571C2218yes—
60#10622569C2218yes—
61#10622560C2218yescomplemented
62#10622559C2218yescomplemented
63C4×(C2×D11)⋊C4C2218yescomplemented
64#10622546C2218yescomplemented
65#10622288C2218yescomplemented
66#10622282C2218yescomplemented
67#10622271C2218yescomplemented
68#10622259C2218yescomplemented
69C25×C11C2311yescharacteristic
70C24×D11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C22×C22⋊D11—24no—
78C22×C22⋊D11—24no—
79C22×C22⋊D11—42no—
80C22×C22⋊D11C2314yes—
81C23×Dic11—24no—
82C23×Dic11—24no—
83C23×Dic11—24no—
84C23×Dic11C2314yes—
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C22×C4×D11—24no—
93C22×C4×D11—24no—
94C22×C4×D11—42no—
95C22×C4×D11C2314yes—
96C22×Dic22—24no—
97C22×Dic22—24no—
98C22×Dic22—42no—
99C22×Dic22C2314yes—
100C2×C11×C4⋊C4—24no—
101C2×C11×C4⋊C4C2314yes—
102C2×C11×C22⋊C4—24no—
103C2×C11×C22⋊C4—24no—
104C2×C11×C22⋊C4—42no—
105C2×C11×C22⋊C4C2314yes—
106C2×C11×C22⋊C4C2314yes—
107C2×C11×C22⋊C4C2314yes—
108C2×C42×C11—42no—
109C2×C42×C11C2314yes—
110C2×C22⋊Dic11—24no—
111C2×C22⋊Dic11—24no—
112C2×C22⋊Dic11C2314yes—
113C2×C22⋊Dic11C2314yes—
114C2×(C2×D11)⋊C4—24no—
115C2×(C2×D11)⋊C4—24no—
116C2×(C2×D11)⋊C4—24no—
117C2×(C2×D11)⋊C4—24no—
118C2×(C2×D11)⋊C4—24no—
119C2×(C2×D11)⋊C4C2314yes—
120C2×(C2×D11)⋊C4C2314yes—
121C2×(C2×D11)⋊C4C2314yes—
122C2×(C2×D11)⋊C4C2314yes—
123C2×(C2×D11)⋊C4C2314yes—
124C2×Dic11⋊C4—24no—
125C2×Dic11⋊C4—24no—
126C2×Dic11⋊C4—24no—
127C2×Dic11⋊C4—42no—
128C2×Dic11⋊C4D418yescomplemented
129C2×Dic11⋊C4C2314yes—
130C2×Dic11⋊C4C2314yes—
131C2×Dic11⋊C4C2314yes—
132C2×Dic11⋊C4C2314yes—
133C2×Dic11⋊C4C2314yes—
134C2×C4×Dic11—24no—
135C2×C4×Dic11—24no—
136C2×C4×Dic11C2314yes—
137C2×C4×Dic11C2314yes—
138#66949—232no—
139#66930—232no—
140C11×#95C2314yes—
141C11×#95C2314yes—
142C11⋊#95C2314yes—
143C11⋊#95C2314yes—
144C11⋊#95C2314yes—
145C11⋊#95C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C2×#2477—111nomaximal, Sylow
153C24×C11—22no—
154C24×C11—22no—
155C24×C11—22no—
156C24×C11—22no—
157C24×C11—22no—
158C24×C11—22no—
159C24×C11#4114yes—
160C24×C11C2412yes—
161C24×C11C2411yescharacteristic
162C23×D11—22no—
163C23×D11—22no—
164C23×D11—22no—
165C23×D11—22no—
166C23×D11—22no—
167C23×D11—22no—
168C23×D11#4114yes—
169C23×D11C2412yes—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—22no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11C2×D414yes—
188C22×C4×C11C2412yes—
189C22×C4×C11C2412yes—
190C22×C4×C11C2412yes—
191C22×C4×C11C2412yes—
192C22×C4×C11C2412yes—
193C22×C4×C11C2412yes—
194C2×C22⋊D11—28no—
195C2×C22⋊D11—28no—
196C2×C22⋊D11—44no—
197C2×C22⋊D11—416no—
198C22×Dic11—232no—
199C22×Dic11—28no—
200C22×Dic11—28no—
201C22×Dic11—22no—
202C22×Dic11—22no—
203C22×Dic11—22no—
204C22×Dic11—22no—
205C22×Dic11—28no—
206C22×Dic11—22no—
207C22×Dic11—22no—
208C22×Dic11—22no—
209C22×Dic11—22no—
210C22×Dic11—22no—
211C22×Dic11—22no—
212C22×Dic11—22no—
213C22×Dic11—22no—
214C22×Dic11—22no—
215C22×Dic11—22no—
216C22×Dic11—22no—
217C22×Dic11—22no—
218C22×Dic11—22no—
219C22×Dic11C2×D414yes—
220C22×Dic11C2×D414yes—
221C22×Dic11#4114yes—
222C22×Dic11#4114yes—
223C22×Dic11C2412yes—
224C22×Dic11C2412yes—
225C22×Dic11C2412yes—
226C22×Dic11C2412yes—
227C22×Dic11C2412yes—
228C22×Dic11C2412yes—
229C22×Dic11C2412yes—
230C2×C4×D11—28no—
231C2×C4×D11—28no—
232C2×C4×D11—44no—
233C2×C4×D11—416no—
234C2×Dic22—28no—
235C2×Dic22—28no—
236C2×Dic22—44no—
237C2×Dic22—416no—
238C11×C4⋊C4—28no—
239C11×C22⋊C4—28no—
240C11×C22⋊C4—28no—
241C11×C22⋊C4—44no—
242C42×C11—44no—
243C22⋊Dic11—28no—
244C22⋊Dic11—28no—
245(C2×D11)⋊C4—28no—
246(C2×D11)⋊C4—28no—
247(C2×D11)⋊C4—28no—
248(C2×D11)⋊C4—28no—
249(C2×D11)⋊C4—28no—
250Dic11⋊C4—28no—
251Dic11⋊C4—28no—
252Dic11⋊C4—28no—
253Dic11⋊C4—44no—
254Dic11⋊C4C2×D4116yescomplemented
255C4×Dic11—28no—
256C4×Dic11—28no—
257C22×C22⋊Q8—111no—
258C22×#117—111no—
259#2477—1116no—
260C2×#400—111no—
261C2×#397—111no—
262C2×#394—111no—
263C2×#393—111no—
264C2×#391—111no—
265C2×#388—111no—
266C2×#388D1111yescharacteristic, complemented
267C2×#387—111no—
268C2×#387—111no—
269C2×#386—111no—
270C2×#386—111no—
271C2×#385—111no—
272C2×C4×C22⋊C4—111no—
273C23×C11—28no—
274C23×C11—28no—
275C23×C11—28no—
276C23×C11—22no—
277C23×C11—22no—
278C23×C11—22no—
279C23×C11—22no—
280C23×C11—22no—
281C23×C11—22no—
282C23×C11—44no—
283C23×C11—44no—
284C23×C11—44no—
285C23×C11—44no—
286C23×C11C22×D412yes—
287C23×C11C2×#4114yes—
288C23×C11C2×#4112yes—
289C23×C11C2×#4112yes—
290C23×C11C2×#4112yes—
291C23×C11C2×#4112yes—
292C23×C11H(5,𝔽2)12yes—
293C23×C112−1+412yes—
294C23×C11C2511yescharacteristic
295C22×D11—28no—
296C22×D11—28no—
297C22×D11—28no—
298C22×D11—22no—
299C22×D11—22no—
300C22×D11—22no—
301C22×D11—22no—
302C22×D11—22no—
303C22×D11—22no—
304C22×D11—44no—
305C22×D11—44no—
306C22×D11—44no—
307C22×D11—44no—
308C22×D11C2×#4114yes—
309C2×C4×C11—28no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—44no—
328C2×C4×C11—44no—
329C2×C4×C11—44no—
330C2×C4×C11—44no—
331C2×C4×C11—44no—
332C2×C4×C11C22×D414yes—
333C22⋊D11—416no—
334C2×Dic11—232no—
335C2×Dic11—28no—
336C2×Dic11—28no—
337C2×Dic11—28no—
338C2×Dic11—28no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—44no—
357C2×Dic11—44no—
358C2×Dic11—44no—
359C2×Dic11C22×D414yes—
360C2×Dic11C22×D414yes—
361C2×Dic11C2×#4114yes—
362C2×Dic11C2×#4114yes—
363C4×D11—416no—
364Dic22—416no—
365C23×Q8—111no—
366C23×D4—111no—
367C24×C4—111no—
368C24×C4—111no—
369C2×C22⋊Q8—118no—
370C2×C22⋊Q8—228no—
371C2×#117—118no—
372C2×#117—228no—
373C22×C4⋊C4—111no—
374C22×C4⋊C4—111no—
375C22×C4⋊C4—111no—
376C22×C4⋊C4—111no—
377C22×C4⋊C4—111no—
378C22×C4⋊C4C2×D1111yescharacteristic
379C22×C22⋊C4—111no—
380C22×C22⋊C4—111no—
381C22×C22⋊C4—111no—
382C22×C22⋊C4—111no—
383C22×C22⋊C4—111no—
384C22×C22⋊C4—111no—
385C22×C22⋊C4—111no—
386C22×C22⋊C4C2×D1111yescharacteristic
387C22×C22⋊C4C2×D1111yescharacteristic
388C22×C22⋊C4C2×D1111yescharacteristic
389C22×C42—111no—
390C22×C42—111no—
391C22×C42C2×D1111yescharacteristic
392#400—118no—
393#397—118no—
394#394—118no—
395#393—118no—
396#391—118no—
397#388—118no—
398#388C2×D1118yescomplemented
399#387—118no—
400#387—118no—
401#386—118no—
402#386—118no—
403#385—118no—
404C4×C22⋊C4—118no—
405C2×#95—111no—
406C2×#95—111no—
407C2×#95—111no—
408C2×#95—111no—
409C2×#95—111no—
410C2×#95—111no—
411C2×#95—111no—
412C2×#95—111no—
413C2×#95—111no—
414C2×#95—111no—
415C2×#95C2×D1111yescharacteristic
416C2×#95C2×D1111yescharacteristic
417C22×C11—24no—
418C22×C11—24no—
419C22×C11—24no—
420C22×C11—42no—
421C22×C11—42no—
422C22×C11—42no—
423C22×C11—42no—
424C22×C11—416no—
425C22×C11#52514yes—
426C22×C11#52914yes—
427C22×C11#54214yes—
428C22×C11#54614yes—
429C22×C11#54814yes—
430C22×C11#55114yes—
431C22×C11#55214yes—
432C22×C11C23×D411yescharacteristic
433C22×C11C22×#4111yescharacteristic
434C22×C11C22×#4111yescharacteristic
435C22×C11C22×#4111yescharacteristic
436C22×C11C22×#4111yescharacteristic
437C22×C11C2×H(5,𝔽2)11yescharacteristic
438C22×C11C2×2−1+411yescharacteristic
439C2×D11—24no—
440C2×D11—24no—
441C2×D11—24no—
442C2×D11—42no—
443C2×D11—42no—
444C2×D11—42no—
445C2×D11—42no—
446C2×D11—416no—
447C4×C11—24no—
448C4×C11—42no—
449C4×C11—42no—
450C4×C11—42no—
451C4×C11—42no—
452C4×C11—42no—
453Dic11—24no—
454Dic11—24no—
455Dic11—24no—
456Dic11—24no—
457Dic11—42no—
458Dic11—42no—
459Dic11—42no—
460C25—111no—
461C25C22×D1111yescharacteristic
462C22×Q8—114no—
463C22×Q8—224no—
464C22×Q8—224no—
465C22×Q8—442no—
466C22×D4—114no—
467C22×D4—224no—
468C22×D4—224no—
469C22×D4—442no—
470C23×C4—111no—
471C23×C4—111no—
472C23×C4—111no—
473C23×C4—111no—
474C23×C4—114no—
475C23×C4—111no—
476C23×C4—111no—
477C23×C4—111no—
478C23×C4—114no—
479C23×C4—224no—
480C23×C4—224no—
481C23×C4—224no—
482C23×C4—224no—
483C23×C4—224no—
484C23×C4—442no—
485C23×C4C22×D1111yescharacteristic
486C23×C4C22×D1111yescharacteristic
487C23×C4C22×D1111yescharacteristic
488C23×C4C22×D1111yescharacteristic
489C23×C4C22×D1111yescharacteristic
490C23×C4C22×D1111yescharacteristic
491C22⋊Q8—2232no—
492#117—2232no—
493C2×C4⋊C4—24no—
494C2×C4⋊C4—118no—
495C2×C4⋊C4—114no—
496C2×C4⋊C4—114no—
497C2×C4⋊C4—114no—
498C2×C4⋊C4—114no—
499C2×C4⋊C4—114no—
500C2×C4⋊C4—224no—
501C2×C4⋊C4—224no—
502C2×C4⋊C4—224no—
503C2×C4⋊C4—442no—
504C2×C4⋊C4C22×D1114yes—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4—114no—
509C2×C22⋊C4—114no—
510C2×C22⋊C4—114no—
511C2×C22⋊C4—114no—
512C2×C22⋊C4—114no—
513C2×C22⋊C4—114no—
514C2×C22⋊C4—114no—
515C2×C22⋊C4—224no—
516C2×C22⋊C4—224no—
517C2×C22⋊C4—224no—
518C2×C22⋊C4—224no—
519C2×C22⋊C4—224no—
520C2×C22⋊C4—224no—
521C2×C22⋊C4—224no—
522C2×C22⋊C4C22×D1114yes—
523C2×C22⋊C4C22×D1114yes—
524C2×C22⋊C4C22×D1114yes—
525C2×C42—42no—
526C2×C42—114no—
527C2×C42—114no—
528C2×C42—224no—
529C2×C42—224no—
530C2×C42C22×D1114yes—
531#95—114no—
532#95—114no—
533#95—114no—
534#95—114no—
535#95—114no—
536#95—114no—
537#95—114no—
538#95—114no—
539#95—114no—
540#95—114no—
541#95C22×D1114yes—
542#95C22×D1114yes—
543C2×C11—44no—
544C2×C11#247718yescomplemented
545C2×C11C2×#52511yescharacteristic
546C2×C11C2×#52911yescharacteristic
547C2×C11C2×#54211yescharacteristic
548C2×C11C2×#54611yescharacteristic
549C2×C11C2×#54811yescharacteristic
550C2×C11C2×#55111yescharacteristic
551C2×C11C2×#55211yescharacteristic
552D11—44no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—114no—
560C24—112no—
561C24—222no—
562C24—222no—
563C24—222no—
564C24—222no—
565C24—222no—
566C24—222no—
567C24#433914yes—
568C24C23×D1112yes—
569C24C23×D1111yescharacteristic
570C2×Q8—228no—
571C2×Q8—228no—
572C2×Q8—444no—
573C2×Q8—4416no—
574C2×D4—228no—
575C2×D4—228no—
576C2×D4—444no—
577C2×D4—4416no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—114no—
596C22×C4—114no—
597C22×C4—114no—
598C22×C4—114no—
599C22×C4—112no—
600C22×C4—112no—
601C22×C4—112no—
602C22×C4—112no—
603C22×C4—112no—
604C22×C4—112no—
605C22×C4—112no—
606C22×C4—228no—
607C22×C4—228no—
608C22×C4—228no—
609C22×C4—2232no—
610C22×C4—228no—
611C22×C4—222no—
612C22×C4—222no—
613C22×C4—222no—
614C22×C4—222no—
615C22×C4—222no—
616C22×C4—222no—
617C22×C4—222no—
618C22×C4—222no—
619C22×C4—222no—
620C22×C4—222no—
621C22×C4—222no—
622C22×C4—222no—
623C22×C4—222no—
624C22×C4—222no—
625C22×C4—222no—
626C22×C4—222no—
627C22×C4—222no—
628C22×C4—228no—
629C22×C4—444no—
630C22×C4—4416no—
631C22×C4D4×D1114yes—
632C22×C4C23×D1112yes—
633C22×C4C23×D1112yes—
634C22×C4C23×D1112yes—
635C22×C4C23×D1112yes—
636C22×C4C23×D1112yes—
637C22×C4C23×D1112yes—
638C4⋊C4—28no—
639C4⋊C4—1116no—
640C4⋊C4—228no—
641C4⋊C4—228no—
642C4⋊C4—228no—
643C4⋊C4—444no—
644C22⋊C4—28no—
645C22⋊C4—28no—
646C22⋊C4—44no—
647C22⋊C4—228no—
648C22⋊C4—228no—
649C22⋊C4—228no—
650C22⋊C4—228no—
651C22⋊C4—228no—
652C22⋊C4—228no—
653C22⋊C4—228no—
654C42—44no—
655C42—228no—
656C42—228no—
657C11C2×#247711yescharacteristic, complemented, Sylow
658C23—28no—
659C23—28no—
660C23—28no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—114no—
672C23—228no—
673C23—228no—
674C23—222no—
675C23—222no—
676C23—222no—
677C23—222no—
678C23—222no—
679C23—222no—
680C23—228no—
681C23—444no—
682C23—444no—
683C23—444no—
684C23—444no—
685C23C2×#433914yes—
686C23C2×#433912yes—
687C23C2×D4×D1112yes—
688C23#6703712yes—
689C23#41×D1112yes—
690C23#41×D1112yes—
691C23#41×D1112yes—
692C23#6704312yes—
693C23C24×D1111yescharacteristic
694Q8—4416no—
695D4—4416no—
696C2×C4—28no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—114no—
720C2×C4—114no—
721C2×C4—114no—
722C2×C4—114no—
723C2×C4—2232no—
724C2×C4—228no—
725C2×C4—228no—
726C2×C4—228no—
727C2×C4—228no—
728C2×C4—222no—
729C2×C4—222no—
730C2×C4—222no—
731C2×C4—222no—
732C2×C4—222no—
733C2×C4—222no—
734C2×C4—222no—
735C2×C4—222no—
736C2×C4—222no—
737C2×C4—222no—
738C2×C4—222no—
739C2×C4—222no—
740C2×C4—222no—
741C2×C4—222no—
742C2×C4—222no—
743C2×C4—222no—
744C2×C4—222no—
745C2×C4—4416no—
746C2×C4—444no—
747C2×C4—444no—
748C2×C4—444no—
749C2×C4C2×D4×D1114yes—
750C22—24no—
751C22—24no—
752C22—24no—
753C22—42no—
754C22—42no—
755C22—416no—
756C22—42no—
757C22—42no—
758C22—224no—
759C22—224no—
760C22—224no—
761C22—442no—
762C22—442no—
763C22—442no—
764C22—4416no—
765C22—442no—
766C22#1062306214yes—
767C22#1062307814yes—
768C22#1062308714yes—
769C22#1062314114yes—
770C22#1062319314yes—
771C22#1062320814yes—
772C22#1062323714yes—
773C22C22×#433911yescharacteristic
774C22C22×D4×D1111yescharacteristic
775C22C2×#6703711yescharacteristic
776C22C2×#41×D1111yescharacteristic
777C22C2×#41×D1111yescharacteristic
778C22C2×#41×D1111yescharacteristic
779C22C2×#6704311yescharacteristic
780C4—24no—
781C4—42no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—224no—
787C4—224no—
788C4—224no—
789C4—224no—
790C4—442no—
791C4—442no—
792C4—442no—
793C2—44no—
794C2—444no—
795C2#1307282318yesdirect product factor
796C2C2×#1062307811yescharacteristic
797C2C2×#1062323711yescharacteristic
798C2C2×#1062319311yescharacteristic
799C2C2×#1062314111yescharacteristic
800C2C2×#1062320811yescharacteristic
801C2C2×#1062308711yescharacteristic
802C2C2×#1062306211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#388C2
socleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#388D11
hypocenterC11C2×#2477
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#66949C2semidirect
2. C22×#66930C2semidirect
3. #13072823C2direct (N × H)
4. C2×#10622271C2semidirect
5. C2×#10622288C2semidirect
7. C2×#10622560C2semidirect
8. C2×#10622259C2semidirect
9. C2×#10622282C2semidirect
10. C2×#10622546C2semidirect
11. C2×#10622591C2semidirect
14. C2×#10622559C2semidirect
15. C2×C4×(C2×D11)⋊C4C2semidirect
16. C2×C11×#388C2semidirect
41. C2×#66949C22semidirect
43. C2×#66930C22semidirect
44. C11×#388C22semidirect
57. #10622591C22semidirect
61. #10622560C22semidirect
62. #10622559C22semidirect
63. C4×(C2×D11)⋊C4C22semidirect
64. #10622546C22semidirect
65. #10622288C22semidirect
66. #10622282C22semidirect
67. #10622271C22semidirect
68. #10622259C22semidirect
128. C2×Dic11⋊C4D4semidirect
254. Dic11⋊C4C2×D4semidirect
266. C2×#388D11semidirect
398. #388C2×D11semidirect
544. C2×C11#2477semidirect
657. C11C2×#2477semidirect
795. C2#13072823direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#669492
C22×#669302
#130728232
C2×#106222712
C2×#106222882
C2×#106225722
C2×#106225602
C2×#106222592
C2×#106222822
C2×#106225462
C2×#106225912
C2×#106225712
C2×#106225692
C2×#106225592
C2×C4×(C2×D11)⋊C42
C2×C11×#3882
C2×#247711